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Feature descriptors of point clouds are used in several applications, such as registration and part segmentation of 3D point clouds. Learning discriminative representations of local geometric features is unquestionably the most important task for accurate point cloud analyses. However, it is challenging to develop rotation or scale-invariant descriptors. Most previous studies have either ignored rotations or empirically studied optimal scale parameters, which hinders the applicability of the methods for real-world datasets. In this paper, we present a new local feature description method that is robust to rotation, density, and scale variations. Moreover, to improve representations of the local descriptors, we propose a global aggregation method. First, we place kernels aligned around each point in the normal direction. To avoid the sign problem of the normal vector, we use a symmetric kernel point distribution in the tangential plane. From each kernel point, we first projected the points from the spatial space to the feature space, which is robust to multiple scales and rotation, based on angles and distances. Subsequently, we perform graph convolutions by considering local kernel point structures and long-range global context, obtained by a global aggregation method. We experimented with our proposed descriptors on benchmark datasets (i.e., ModelNet40 and ShapeNetPart) to evaluate the performance of registration, classification, and part segmentation on 3D point clouds. Our method showed superior performances when compared to the state-of-the-art methods by reducing 70$\%$ of the rotation and translation errors in the registration task. Our method also showed comparable performance in the classification and part-segmentation tasks with simple and low-dimensional architectures.